Question: William is 18 years older than Ishaan. Nineteen years ago, William was 3 times as old as Ishaan. How old is Ishaan now?
Solution: We can use the given information to write down two equations that describe the ages of William and Ishaan. Let William's current age be $w$ and Ishaan's current age be $i$ The information in the first sentence can be expressed in the following equation: $w = i + 18$ Nineteen years ago, William was $w - 19$ years old, and Ishaan was $i - 19$ years old. The information in the second sentence can be expressed in the following equation: $w - 19 = 3(i - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to use our first equation for $w$ and substitute it into our second equation. Our first equation is: $w = i + 18$ . Substituting this into our second equation, we get the equation: $(i + 18)$ $-$ $19 = 3(i - 19)$ which combines the information about $i$ from both of our original equations. Simplifying both sides of this equation, we get: $i - 1 = 3 i - 57$ Solving for $i$ , we get: $2 i = 56$ $i = 28$.